Chapter 13, Problem 13.55P

Two concentric spheres of diameter $D_1=0.8m$ and $D_2=1.2m$ are separated by an air space and have surface temperatures of $T_1=400K$ and $T_2=300K$ .
(a) If the surfaces are black, what is the net rate of radiation exchange between the spheres?
(b) What is the net rate of radiation exchange between the surfaces if they are diffuse and gray with ${\epsilon }_1=0.5$ and ${\epsilon }_2=0.05$ ?
(c) What is the net rate of radiation exchange if $D_2$ is increased to 20 m, with ${\epsilon }_2=0.05$ , ${\epsilon }_1=0.5$ , and $D_1=0.8m$ ? What error would be introduced by assuming blackbody behavior for the outer surface $({\epsilon }_2=1)$ , with all other conditions remaining the same?
(d) For $D_2=1.2m$ and emissivities of ${\epsilon }_1=0.1,0.5,$ and 1.0, compute and plot the net rate of radiation exchange as a function of ${\epsilon }_2$ for $0.05\le {\epsilon }_2\le 1.0$ .